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REVIEW 4 major objections 5 minor 90 references

Hierarchy or Heterarchy? A Theory of Long-Range Connections for the Sensorimotor Brain

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper argues that every cortical column learns complete objects and the thalamus is a pose converter, making the neocortex a heterarchy.

desk verdict A clear, honest speculative theory of cortical long-range connections with a load-bearing but unproven mapping from L6a/L6b to object-relative pose; the anatomy review is solid, the theory deserves referee time. read the letter →

arxiv 2507.05888 v1 pith:7QRXVHRE submitted 2025-07-08 q-bio.NC cs.AI

Jeff Hawkins (1) , Niels Leadholm (1) , Viviane Clay (1) ((1) Thousand Brains Project) This is my paper
classification q-bio.NCcs.AI
keywords SensorimotorNeocortexThalamusLong-RangeConnectionsHierarchyHeterarchyReferenceFramesCanonicalMicrocircuit
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Traditional accounts treat the neocortex as a feedforward hierarchy in which low-level regions detect features and only high regions represent complete objects. This paper argues instead that every cortical column is a sensorimotor system that learns full object models by integrating sensation with movement, so even V1 and V2 can recognize complete 3D objects. On this view, hierarchical connections between regions do not build features into objects; they bind already-known child objects into parent objects at each location. The paper further claims that the thalamus is not a passive relay but performs the moment-by-moment rotation of sensory, movement, and motor signals between egocentric and allocentric reference frames, using orientation information from layer 6b. If correct, the cortex is best described as a heterarchy: the same pair of regions can act hierarchically for composition and in parallel for consensus at the same time.

What carries the argument

The load-bearing mechanism is the Thousand Brains Theory account of a cortical column: L4 binds sensed features to location signals in L6a, L3 pools across movements to represent the object, and L6b encodes the sensor's orientation relative to the object. Long-range connections are then read as implementing three computations: feedforward L3-to-L4 projections send child-object identity up, feedback L6a-to-L1 projections predict the child object and its location, L6b-to-thalamus projections tell relay cells which egocentric-to-allocentric rotation to apply, L5a motor output carries an allocentric-to-egocentric motor command with an efference copy routed through the thalamus, and same-layer L3 projections let columns vote on object identity. The key mapping is the assignment of abstract variables such as location, orientation, and object identity to specific cell populations and layers.

What would settle it

Record from identified L6b neurons in V1 or S1 while an animal fixates or touches a known object and the sensor is rotated relative to the object with the object's identity and sensed location held constant; if L6b firing does not track the sensor-to-object orientation, the proposed mechanism for thalamic pose conversion and for computing child-to-parent orientation lacks its stated neural substrate.

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Extended reading notes

Core claim

The paper's central claim is that the neocortex should be understood as a heterarchy of sensorimotor columns rather than a hierarchy of feature detectors. Each column receives sensory features and movement data through the thalamus and learns complete object models by pairing features with the sensor's location and orientation on the object. Because every region receives driving thalamic input, primary and secondary regions can represent complete objects in parallel; the laminar-asymmetric cortico-cortical connections then let a higher region assign a child object represented in a lower region to a location on a parent object, learning compositional structure location by location. The same logic assigns a new role to the thalamus: relay cells convert sensory and motor data from egocentric to allocentric coordinates, and converging layer 6b projections from two hierarchically adjacent columns let the thalamus compute the relative orientation between child and parent objects. The paper concludes that the long-range connections of the cortex implement three computations: reference-frame transformation, compositional learning, and rapid consensus among columns.

Load-bearing premise

The theory assigns abstract computational roles to specific cell populations—L6a as the sensor's location on the object and L6b as the sensor's orientation relative to the object—and then builds the entire account of thalamic pose transformation and compositional learning on that assignment, without direct experimental evidence that these layers carry these signals.

Editorial extensions

If this is right

  • Even primary sensory regions should contain neurons that represent whole objects, so object-selective responses in V1 or S1 should be found in freely moving animals that have learned the object, not only in downstream regions.
  • Thalamic relay cells should be found to transform the orientation of incoming sensory and motor signals, so thalamic inactivation or misdirection should produce systematic, orientation-dependent perceptual and motor errors.
  • Learning a new composition such as a logo on a mug should require only binding two existing models at each fixated location, so the brain should not need to relearn the child object when the parent changes.
  • The motor system is not confined to motor cortex: every cortical column should have a layer 5a output, and copies of these motor commands should reach higher columns through the thalamus.
  • A pair of connected regions can be simultaneously hierarchical and parallel, so experimental measures of hierarchy based on laminar connectivity alone do not tell the whole story about how two regions cooperate.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the paper is right, passive-viewing experiments that immobilize an animal will systematically under-represent object knowledge in primary sensory cortex, because object representations only become visible when the sensor moves and updates location and orientation signals.
  • The theory suggests a concrete test for AI: a sensorimotor system with explicit layer-6b-like orientation variables and local Hebbian updates should learn compositional variations such as bent or scaled logos in a few fixations, whereas a feedforward network would need to see many augmented examples.
  • The paper leaves dynamic objects to future work; if static composition is learned location by location, the same machinery would presumably need to store time-varying poses, which might be testable by asking whether the cortex reuses the same L6b-thalamus circuit for predicting motion trajectories.
  • A further implication the authors do not draw is that kinematic history should shape object representations even in early sensory areas, so motor experience should be treated as a variable in neural decoding studies.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. This paper argues against a purely hierarchical model of neocortical organization, proposing instead a heterarchical view under the Thousand Brains Theory (TBT). The authors review four classes of long-range connections (hierarchical cortico-cortical, non-hierarchical cortico-cortical, cortico-thalamic, and layer 5 motor connections) and assign each a specific functional role: L6a cells are proposed to encode the location of a sensor on an object, L6b cells to encode the orientation of the sensor relative to the object; thalamic relay cells are proposed to rotate incoming sensory and motor information from egocentric to allocentric coordinates based on L6b input; hierarchical connections are proposed to learn compositional parent–child object structure; and non-hierarchical connections are proposed to implement a 'voting' mechanism for rapid consensus among columns. The paper concludes that the neocortex is best described as a heterarchy in which regions act both hierarchically and in parallel.

Significance. If the proposed mapping of representational content to L6a/L6b and the thalamic pose-converter hypothesis were empirically supported, the paper would provide a substantial reconceptualization of the roles of layer 6 and the thalamus, with broad implications for both neuroscience and AI. The anatomical review in §2 is a useful synthesis of a large literature, and the paper is commendably explicit about which pieces are novel and speculative. The framework is falsifiable in principle: for example, it predicts object-relative, head-direction-like tuning in L6b neurons and that primary visual cortex contains complete object models. However, the central representational assignments are asserted from TBT priors rather than derived, and no mechanistic simulation or direct experimental evidence is provided; the paper's own statements ('This is the first time we have proposed this role for the thalamus', 'our best guess') flag the fragility of these load-bearing assumptions.

major comments (4)
  1. [§3.1] The assignment of abstract variables to specific cell populations—L6a as sensor-location (grid-like) and L6b as sensor-orientation (head-direction-like) relative to an object—is the load-bearing premise for the entire account, but it is supported only by plausibility and by connections. The cited anatomical findings (L4–L6a associativity, L6b→thalamus/L5a projections) establish pathways, not representations. The paper itself flags this novelty ('This is the first time we have proposed this role for the thalamus', §3.1) and the scale mechanism as 'our best guess' (§3.3.3). Because the proposed functions of the thalamus, the L5a motor transform, and the compositional hierarchy all depend on this mapping, the paper needs to provide testable, specific predictions (e.g., L6b neurons should show object-centered orientation tuning that rotates with the object's orientation in memory) or a simulation showing that the proposed connectivity could implement the required transformations.
  2. [§2.2/§3.2] The proposal that thalamic relay cells perform a continuous orientation-dependent rotation of high-dimensional feature and movement vectors is inconsistent with the paper's earlier statement that layer 6 cortico-thalamic projections are modulatory and do not directly drive relay cells (§2.2, citing Sherman, 2005). A modulatory input can change gain or bias, but the paper offers no equation, simulation, or circuit-level mechanism showing how an L6b signal could implement a rotation of a population code in real time. This gap is load-bearing for the central claim of the thalamus as a pose converter, and it is directly testable: for example, one could predict that inactivating L6b should abolish rotation-dependent changes in relay-cell responses. The authors should either provide a concrete mechanism (e.g., a gain-field model) or soften the claim to a functional-level hypothesis explicitly needing implementation.
  3. [§3.3] The explanation of hierarchical connections in terms of compositional object learning is largely a restatement of the Thousand Brains framework rather than an independent derivation. The paper takes as given that each column learns complete object models (motivated by TBT, §3.1), and then assigns functions to connections in a way that follows directly from that assumption. This circularity is acknowledged implicitly by the authors' reliance on TBT as a starting point, but it weakens the claim that the proposal is 'a new interpretation of how sensory and motor information is processed' (Abstract). To break the circularity, the paper must state at least one prediction that is not already implied by the TBT premise—for example, that L3 outputs (which the paper identifies as object IDs) should carry decodable object identity independent of feature content, or that the hierarchical feedforward/feedback asymmetry in laminar targeting should vary with the compositionality of the learned relationship. Without such independent predictions, the 'explanation' of long-range connections is unfalsifiable and indistinguishable from the framework it is derived from.
  4. [§3.3.3] The proposed mechanism for computing the relative scale of child and parent objects at each location is too underspecified to evaluate. The paper states that scale is calculated via oscillatory interference, citing Burgess et al. (2007), but provides no account of how two oscillators in the thalamus would encode scale differences or how changing the frequency of an oscillator would lead to a learned relative-scale value in the cortex. This is acknowledged as 'our best guess,' but it is presented as a central part of the compositional model. The authors should either specify the computation in enough detail to be modeled or explicitly mark the entire scale-calculation subsection as a non-committal speculation awaiting further work.
minor comments (5)
  1. [§2.2] The citation '(Murray Sherman, 2001)' in the text should be '(Sherman, 2001)' to match the reference list consistently.
  2. [§3.2] The word 'therefor' in 'different parts of the skin can move independently and therefor have different orientations' should be 'therefore'.
  3. [References] The reference 'V oges, N., Schüz, A., Aertsen, A., and Rotter, S. (2010)' contains a stray space in the author name; it should be 'Voges'.
  4. [Figure 5] The caption lists the magnocellular pathway, vestibular system, and superior colliculus as sources of movement input, but the figure does not clearly indicate how these three sources are combined; a sentence clarifying the schematic relationship would improve readability.
  5. [§3.4] The term 'flash inference' is used without a formal definition or a reference; please either define it in the text or cite a prior source.

Circularity Check

2 steps flagged · score 6.0 of 10

The new functional assignments are explicit proposals, but the key mechanism is self-definitional: L6b is posited to encode object-relative orientation, and that same posited code is then used to 'explain' the L6b-to-thalamus transform; the framework also leans heavily on self-cited Thousand Brains Theory.

  1. self definitional [§3.1–§3.2 (Figs. 4–5)]
    "We propose that cells in L6a represent the sensor’s location on the object, and cells in L6b represent the orientation of the sensor relative to the object. ... Since L6b represents the orientation of the sensor to the object, projections from L6b to the thalamus ... tell the thalamic relay cells what orientation transform is needed."

    The explanation of the L6b-to-thalamus pathway reduces to the paper's own stipulation: L6b is assigned the semantic content 'orientation of the sensor relative to the object' in §3.1, and then the same assigned content is cited in §3.2 as the reason the projection can 'tell the thalamic relay cells what orientation transform is needed.' No independent evidence is provided that L6b neurons carry an object-relative orientation signal; the paper itself marks the proposal as new ('This is the first time we have proposed this role for the thalamus'). The pathway's functional role is therefore a restatement of the posited code, not a conclusion derived from the anatomical facts, which establish connectivity but not representational content.

  2. self citation load bearing [§3.1 Background]
    "We have previously proposed a theory of sensorimotor processing in the neocortex called the Thousand Brains Theory (TBT) (Hawkins et al., 2019; Hawkins, 2021). In this theory, sensorimotor integration occurs in every cortical column."

    The paper's central premise—that every cortical column is a sensorimotor system, and hence that long-range connections implement compositional learning and pose transformation—is imported from the authors' own prior TBT papers. The new assignments to L6a, L6b, and the thalamus are generated to satisfy that framework, so their explanatory force depends on accepting a self-cited model rather than on independent evidence provided here. This is load-bearing, although the paper does offer independent anatomical evidence for parallel cortical processing, so the heterarchy claim is not wholly determined by the self-citation chain.

full rationale

This is a theory-proposal paper with no fitted parameters and no equations, so the 'prediction from fit' pattern does not apply. The main circularity is explanatory and definitional: the paper posits that L6b encodes object-relative orientation, then uses that same posited code to argue that the L6b-to-thalamus projection implements the required orientation transform. The functional role of the pathway is thus a restatement of the assumed code, not a consequence derived from independent data. In addition, the foundational 'every column is a sensorimotor system' claim is taken from the authors' earlier TBT work, which is unverified here and is load-bearing for the subsequent proposals. I do not score this higher because the anatomical review in Section 2 is independent, the heterarchy framing is argued from external evidence about parallel and hierarchical connectivity, and the proposed L6a/L6b/thalamus roles are explicit, testable hypotheses rather than hidden redefinitions of data.

Assumptions & free parameters 0 free parameters · 5 assumptions · 1 invented entities

The ledger captures the unproved premises the theory depends on. Free parameters: none numerical. The main structural assumptions are the Thousand Brains framework and the new mappings of computational variables to L6a/L6b and the thalamus. One invented functional entity, the thalamic pose transformation, is listed with no independent evidence.

assumptions (5)
  • domain assumption Thousand Brains Theory: every cortical column is a sensorimotor learning system that integrates sensory and movement data to learn complete object models.
    Invoked at the start of §3.1 as the foundation of the paper. The theory is cited from the authors' own prior publications and is not independently argued for in this paper.
  • ad hoc to paper L6a cells encode the sensor's location on the object; L6b cells encode the sensor's orientation relative to the object.
    §3.1. This is a new, direct assignment of neural population activity to abstract pose variables, with no supporting experimental evidence cited.
  • ad hoc to paper Thalamic relay cells rotate incoming sensory and motor data from egocentric to allocentric coordinates, regulated by L6b projections.
    §3.2. The paper states this is the first time it has proposed this role for the thalamus; no independent evidence is presented.
  • domain assumption The magnocellular visual pathway provides movement information about the retina relative to the world.
    §3.2.1. Plausible but not established; the paper infers it from broad receptive fields and response properties.
  • ad hoc to paper Relative scale between parent and child objects is computed in the thalamus via oscillatory interference mechanisms.
    §3.3.3. The paper explicitly labels this 'our best guess' and defers details, so it is an openly unvalidated mechanism.
invented entities (1)
  • Thalamic pose transformation (relay cells as coordinate converters)
    purpose: Converts sensory features and motor commands between egocentric and allocentric reference frames, and computes relative pose between child and parent objects during compositional learning.
    Proposed for the first time in this paper (§3.2, §3.3.3). It is inferred from the Thousand Brains framework, and no falsifiable handle or experimental protocol is provided.

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Cite this review

Pith. "Pith review of Hierarchy or Heterarchy? A Theory of Long-Range Connections for the Sensorimotor Brain." pith.science (2026). https://pith.science/paper/7QRXVHRE

@misc{pith2026250705888,
  author       = {Pith},
  title        = {Pith review of: Hierarchy or Heterarchy? A Theory of Long-Range Connections for the Sensorimotor Brain},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7QRXVHRE}},
  note         = {Machine review of arXiv:2507.05888}
}
read the original abstract

In the traditional understanding of the neocortex, sensory information flows up a hierarchy of regions, with each level processing increasingly complex features. Information also flows down the hierarchy via a different set of connections. Although the hierarchical model has significant support, many anatomical connections do not conform to the standard hierarchical interpretation. In addition, hierarchically arranged regions sometimes respond in parallel, not sequentially as would occur in a hierarchy. This and other evidence suggests that two regions can act in parallel and hierarchically at the same time. Given this flexibility, the word "heterarchy" might be a more suitable term to describe neocortical organization. This paper proposes a new interpretation of how sensory and motor information is processed in the neocortex. The key to our proposal is what we call the "Thousand Brains Theory", which posits that every cortical column is a sensorimotor learning system. Columns learn by integrating sensory input over multiple movements of a sensor. In this view, even primary and secondary regions, such as V1 and V2, can learn and recognize complete 3D objects. This suggests that the hierarchical connections between regions are used to learn the compositional structure of parent objects composed of smaller child objects. We explain the theory by examining the different types of long-range connections between cortical regions and between the neocortex and thalamus. We describe these connections, and then suggest the specific roles they play in the context of a heterarchy of sensorimotor regions. We also suggest that the thalamus plays an essential role in transforming the pose between objects and sensors. The novel perspective we argue for here has broad implications for both neuroscience and artificial intelligence.

Figures

Figures reproduced from arXiv: 2507.05888 by the authors.

Figure 1
Figure 1. Classic feedforward (blue) and feedback (purple) pathways illustrated on two cortical columns. In this and [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. There are numerous long-range connections that do not make sense in a classical hierarchy. A) Cells in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Cortico-thalamic connections appear to be both hierarchical and non-hierarchical. A) Layers 6a and 6b project [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Cortical columns integrate sensor and movement information to learn and recognize models. Sensory features [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Feature input (blue) and movement input (pink) must be converted from a sensor’s orientation (dashed lines) [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: A) The classic view of hierarchical processing in the neocortex. Sensor information enters the neocortex via [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: Compositional objects are modeled using hierarchy. A) Learning the relationship of a child object to a [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 2
Figure 2. Figure 2: figure 2. We propose these connections serve two purposes. 1) They allow inference with fewer movements, and 2) they [PITH_FULL_IMAGE:figures/full_fig_p013_2.png]

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    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.